1. Field of the Invention
The present invention relates to a method for measuring the height of a sphere or a hemisphere and, in particular, to a method for measuring the height of a sphere or a hemisphere and for allowing an inexpensive apparatus to measure the uniformity of the height-directional positions of bump electrodes in a semiconductor device of a type such as BGA (ball grid array) and CSP (chip size package or chip scale package) having spherical or hemispherical bump electrodes.
2. Related Art of the Invention
In a semiconductor device of a type such as BGA and CSP joined through bump electrodes, a large number of spherical or hemispherical bump electrodes 11 provided on the back surface of the package 10 of a semiconductor device as shown in FIGS. 5(A) and 5(B) are connected to a large number of substrate electrodes 13 provided on a substrate 12 shown in FIGS. 6(A) and 6(B). In this configuration, troubles that the semiconductor device does not perform desired operation and functions have occurred in some ,cases depending on the state of connection between a large number of the spherical or hemispherical bump electrodes 11 and a large number of the substrate electrodes 13.
This causes the necessity of inspections of the state of connections between a large number of the spherical or hemispherical bump electrodes 11 and a large number of the substrate electrodes 13. Never the less, the height-directional dimension of each bump electrode 11 is as small as a few 100 xcexcm. This prevents the inspection of the state of joining between the bump electrodes 11 and the substrate electrodes 13 in the state that the bump electrodes 11 are connected to the substrate electrodes 13 as shown in FIG. 6(B), unless a special inspection method is used such as X-ray inspection. This situation enhances the importance of the inspection of the height-directional dimensions of the bump electrodes 11 and their uniformity before the connection, in comparison with the case of the other prior art semiconductor devices.
Various types of height-directional dimension measuring apparatuses for bump electrode have been available commercially since a long time ago. These apparatuses achieve a sufficient measurement precision as precise as the order of magnitude of sub-micron by means of pencil beam scan and the like. The time necessary for the measurement is also sufficiently reduced. Nevertheless, they have a complicated mechanism, and hence cause cost problem.
On the other hand, as a distance measuring technique using an imaging system, a principle called xe2x80x9cdepth from focusxe2x80x9d or xe2x80x9cshape from focusxe2x80x9d has been known since a long time ago (see, for example, IEEE Transaction on Pattern Analysis and Machine Intelligence, Vol. 16, No. 8, August 1994, pp. 824-831). In the technique using this principle, with changing the focus setting, the in-focus position of the focus setting is determined such that the blur of an image is minimized, so that the distance to an object is calculated. Various methods for evaluating the degree of focus have been devised so far, and the technique has already been commercialized as auto focus cameras (AFC""s).
Here, the term xe2x80x9cthe degree of focusxe2x80x9d indicates a value obtained by evaluating quantitatively the contrast of each pixel on the basis of the brightness distribution of an image.
In the use of the above-mentioned principle called xe2x80x9cdepth from focusxe2x80x9d or xe2x80x9cshape from focusxe2x80x9d, the in-focus position of the focus setting is searched and selected. That is, (1) a large number of images are acquired with changing the distance between an object and a camera, and then (2) xe2x80x9cthe degree of focusxe2x80x9d is calculated for each of these images for each pixel of interest, so that a position is estimated where xe2x80x9cthe maximum degree of focusxe2x80x9d is obtained. This estimation is performed, in general, using a technique of Gaussian fitting.
Thus, in this prior art method, (1) since plural images are acquired, a longer time is necessary for moving the camera and acquiring the images. Further, (2) the algorithm for estimating the maximum degree of focus causes a heavy load to the processor, and hence increases the process time.
Meanwhile, the absolute values of the height-directional dimensions of the bump electrodes 11 need to fall within a predetermined range relative to a design value. However, the height-directional dimensions themselves can be controlled, for example, by adjusting plating time in case that the bump electrodes 11 are formed by plating, or alternatively by controlling the pre-fusion-joining diameters of metallic balls into a predetermined range in case that the bump electrodes 11 are formed by fusion joining.
Nevertheless, uniformity in the height-directional dimensions of a large number of bump electrodes 11 is difficult to be obtained at sufficient precision because of, for example, a variation in the height-directional dimensions easily caused by a variation in the plating electric current depending on the location of arrangement of the bump electrodes 11 in case that the bump electrodes 11 are formed by plating. Further, in order to ensure the connection characteristic between the bump electrodes 11 and the substrate electrodes 13, the height-directional positions of the top points of a large number of the bump electrodes 11 are more important than the absolute values of respective height-directional dimensions of the bump electrodes 11. More specifically, what is important is uniformity in the height-directional positions of the top points of a large number of the bump electrodes 11.
With considering the a above-mentioned situation, an object of the invention is to provide a method for measuring the height of a sphere or a hemisphere and for permitting sufficiently precise measurement of the uniformity of the height-directional positions of spheres or hemispheres such as bump electrodes of a semiconductor device by means of an apparatus less expensive than prior art apparatuses.
The first aspect of the invention is a method for measuring the height of a sphere or a hemisphere, comprising the steps of: acquiring two images, at diverse height-directional positions of focal plane, of a first sphere or hemisphere and a second sphere or hemisphere; calculating the degree of focus at each point; subtracting the degree of focus of the second image from that of the first image; calculating the contour of horizontal cross sections of the spheres or hemispheres on the basis of the position of equal degree of focus; and calculating the height of the spheres or hemispheres on the basis of the size of the contour.
The term xe2x80x9cthe position of equal degree of focusxe2x80x9d indicates the point where the difference between the degree of focus of the image at the first focusing position and that at the second focusing position acquired in the above-mentioned distance measuring method equals zero. As a result, xe2x80x9cthe position of equal degree of focusxe2x80x9d equals the position of the sphere or the hemisphere at the middle position (height) between the first focal plane and the second focal plane.
In contrast to the prior art, the present method for measuring the height of a sphere or a hemisphere does not measure precisely the height-directional dimension itself of a sphere or a hemisphere. However, the method permits the measurement of the height-directional positions of bump electrodes with a measurement precision of approximately xc2x110 xcexcm, which permits the evaluation of the connection characteristic between the bump electrodes and substrate electrodes. This allows a simple and inexpensive apparatus to evaluate the uniformity of the height-directional positions of a large number of bump electrodes.
The second aspect of the invention is a method for measuring the height of a sphere or a hemisphere, wherein after the degree of focus of the first image is acquired, the sphere or the hemisphere and an imaging system are relatively moved closer or farther, and then the degree of focus of the second image is acquired.
The statement xe2x80x9cthe sphere or the hemisphere and an imaging system are relatively moved closer or fartherxe2x80x9d includes that the sphere or the hemisphere is moved closer to or farther from the imaging system, that the imaging system is moved closer to or farther from the sphere or the hemisphere, and that both of the sphere or the hemisphere and the imaging system are moved closer to or farther from each other.
The present method for measuring the height of a sphere or a hemisphere allows a single imaging system to acquire the degrees of focus of the first and the second images. This reduces the cost of the configuration of the imaging system.
The third aspect of the invention is a method for measuring the height of a sphere or a hemisphere, wherein the degrees of focus of the first and the second images are acquired through a beam splitter by a plurality of imaging systems.
According to the present method for measuring the height of a sphere or a hemisphere, an optical path having a diverse optical path length is formed separately for each of a plurality of the imaging systems by means of the beam splitter. This permits simultaneous acquisition of the degrees of focus of the first and the second images by means of a plurality of the imaging systems. This avoids the necessity of moving relatively the sphere or the hemisphere and the imaging system closer or farther after the first image is acquired. This simplifies the operation, and reduces the height measurement time.
The fourth aspect of the invention is a method for measuring the height of a sphere or a hemisphere, wherein the degrees of focus of a first color image and a second color image having an optical path length difference through a glass substrate having a color-dependent refractive index are acquired by a color imaging system.
According to the present method for measuring the height of a sphere or a hemisphere, the optical path length difference caused by the color-dependent refractive index of the glass substrate is utilized. This allows the color imaging system composed of two or three CCD""s to acquire the degrees of focus of the first and the second images simultaneously. This avoids the necessity of moving relatively the sphere or the hemisphere and the imaging system closer or farther. This simplifies the operation, and reduces the height measurement time. The size of the apparatus is also reduced.
The fifth aspect of the invention is a method for measuring the height of a sphere or a hemisphere, wherein the sphere or the hemisphere is a bump electrode of a semiconductor device.
The present method for measuring the height of a sphere or a hemisphere permits sufficiently precise measurement of the uniformity of the height-directional positions of spherical or hemispherical bump electrodes of a semiconductor device by means of an apparatus simpler and less expensive than prior art apparatuses. This reduces the cost of measurement of the uniformity of the height-directional positions of a plurality of bump electrodes.
Further, the present method for measuring the height of a sphere or a hemisphere allows semiconductor device packages having a large variation in the height-directional positions of bump electrodes to be detected and eliminated before the joining of the bump electrodes of semiconductor devices to substrate electrodes. This improves the yield obtained after the joining of bump electrodes to substrate electrodes.